After the upgrade is reported as successfully completing, nothing more than routine checks within the projects are necessary. I would recommend that user check that they can add, edit, and delete entities as necessary and allowed, that the attachments are still intact and available for entities (can be tested by viewing a few entities that have attachments) as necessary and that data is available as expected. If you are using third party tools I would insure that integration is still correct and valid. Other than the above noted, nothing special should be necessary.
Hope this helps,